SOLUTION: The difference of two numbers is 5. The resultwhen the greater number is decreased by twice the lesser is 9. Let x be the greater number and y be the lesser number. Find the number

Question 269481: The difference of two numbers is 5. The resultwhen the greater number is decreased by twice the lesser is 9. Let x be the greater number and y be the lesser number. Find the numbers.
michael 13 years old... need help... confused
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=the greater number
Then y=the lesser number
Now we are told that the difference of the two numbers(greater-lesser) equals 5, so:
x-y=5------------------------eq1
Twice the lesser number is 2y
Now we are also told that when we decrease(make smaller) the greater number by twice the lesser number(x-2y) the result is 9, so:
x-2y=9------------------------eq2
Lets subtract eq1 from eq2 and we get:
-y=4 or
y=-4-------------------lesser number
Substitute y=-4 into eq1 and we get:
x-(-4)=5
x+4=5 subtract 4 from each side
x+4-4=5-4 collect like terms
x=1----------------------- greater number
CK
1-(-4)=1+4=5-----ok
1-(-2*4)=9
1+8=9
9=9------ok

Does this help???--ptaylor
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